On Hochschild type constructions in motivic homotopy theory

In the first part we study a motivic analogue of topological Hochschild homology, which we call motivic Hochschild homology, for normed motivic spectra and its interaction with motivic Thom spectra. We show that the normed motivic Thom construction commutes with motivic Hochschild homology and provide a formula in the case that the base of the motivic Thom spectra is a grouplike normed space. In the second part we study a notion of C-motivic spectra with Gm-action and show that various constructions on the ∞-category of C-motivic spectra SH(C) is compatible with this Gm-equivariant structure. As an application we compute the motivic homotopy Gm-fixed points for a class of examples satisfying a motivic B¨okstedt periodicity condition.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Tan, Johnson

Contributors dc:contributor

• Heller, Jeremiah
• Stojanoska, Vesna
• Rezk, Charles
• Berwick-Evans, Dan

• Motivic
• Homotopy

Statement dc:rights

• Copyright 2025 Johnson Tan

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/130166

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F130166